# Quantum chaos of an ion trapped in a linear ion trap

## Abstract

We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model andmore »

- Authors:

- Theoretical Division T-13, and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Theoretical Division T-4, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20216516

- Resource Type:
- Journal Article

- Journal Name:
- Chaos (Woodbury, N. Y.)

- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 2; Other Information: PBD: Jun 2000; Journal ID: ISSN 1054-1500

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; IONS; TRAPS; LASER RADIATION; RESONANCE; HARMONIC OSCILLATOR MODELS; PHASE SPACE; THEORETICAL DATA

### Citation Formats

```
Berman, Gennady P., James, Daniel F. V., Kamenev, Dimitri I., and Nizhny Novgorod State University, Nizhny Novgorod, 603600, Russia.
```*Quantum chaos of an ion trapped in a linear ion trap*. United States: N. p., 2000.
Web. doi:10.1063/1.166504.

```
Berman, Gennady P., James, Daniel F. V., Kamenev, Dimitri I., & Nizhny Novgorod State University, Nizhny Novgorod, 603600, Russia.
```*Quantum chaos of an ion trapped in a linear ion trap*. United States. doi:10.1063/1.166504.

```
Berman, Gennady P., James, Daniel F. V., Kamenev, Dimitri I., and Nizhny Novgorod State University, Nizhny Novgorod, 603600, Russia. Thu .
"Quantum chaos of an ion trapped in a linear ion trap". United States. doi:10.1063/1.166504.
```

```
@article{osti_20216516,
```

title = {Quantum chaos of an ion trapped in a linear ion trap},

author = {Berman, Gennady P. and James, Daniel F. V. and Kamenev, Dimitri I. and Nizhny Novgorod State University, Nizhny Novgorod, 603600, Russia},

abstractNote = {We describe the transition to quantum chaos of an ion trapped in a linear ion trap and interacting with two laser fields. Under the conditions of adiabatic illumination of the upper level of the ion, and when the frequencies of the two laser beams are slightly different, the system is reduced to a quantum linear oscillator interacting with a monochromatic wave. The property of localization over the quantum resonance cells is proposed to exploit in order to facilitate the process of measurement of the probability distribution of an ion on the vibrational levels. In the regime of strong chaos the time-averaged values of the energy and dispersion of energy are computed and compared with the corresponding classical quantities for different values of the perturbation amplitude. In the exact resonance case, the classical analog of the system possesses an infinite inhomogeneous stochastic web. We analyze the quantum dynamics inside the inhomogeneous web. It is shown that the quantum system mimics on average the dynamics of the corresponding classical system. Formation of the quantum resonance cells is illustrated in the case of a finite detuning from the exact resonance, and under increasing of the wave amplitude. The parameters of the model and the initial conditions are close to the real physical situation which can be realized in the system of cold trapped ion perturbed by two lasers fields with close frequencies. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.166504},

journal = {Chaos (Woodbury, N. Y.)},

issn = {1054-1500},

number = 2,

volume = 10,

place = {United States},

year = {2000},

month = {6}

}